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<h2>Project 3: Reinforcement Learning</h2>

<em>Due <b>3/4</b> at 11:59pm</em><br>

<blockquote>
<center>
<img src="capsule.png" width="50%" alt="capsuleClassic layout"/>
</center>
  <p><cite><center>Pacman seeks reward.<br>
  Should he eat or should he run?<br>
  When in doubt, q-learn.</center></cite></p>
</blockquote>	

<h3>Introduction</h3>

<p>In this project, you will implement value iteration and q-learning. You will test your agents first on Gridworld (from class), then apply them to a simulated robot controller (Crawler) and Pacman.</p>

<p>The code for this project contains the following files, which are available in a <a href="reinforcement.zip">zip archive</a>:</p>

<h5><b> Files you will edit </b></h5> 

<table border="0" cellpadding="10">	
<tr><td><code><a href="docs/valueIterationAgents.html">valueIterationAgents.py</a></code></td>

<td>A value iteration agent for solving known MDPs.</td>

</tr>

<tr>

<td><code><a href="docs/qlearningAgents.html">qlearningAgents.py</a></code></td>

<td>Q-learning agents for Gridworld, Crawler and Pacman</td>

</tr>

<tr>

<td><code><a href="docs/analysis.html">analysis.py</a></code></td>

<td>A file to put your answers to questions given in the project.</td>

</tr>


</table>

<h5><b>Files you should read but NOT edit</b></h5>


<table border="0" cellpadding="10">	
<tr>
<td><code><a href="docs/mdp.html">mdp.py</a></code></td>


<td>Defines methods on general MDPs. </td>

</tr>

<tr>
<td><code><a href="docs/learningAgents.html">learningAgents.py</a></code></td>
<td>Defines the base classes <code>ValueEstimationAgent</code> and <code>QLearningAgent</code>, which your agents will extend.</td>
</tr>

<tr>

<td><code><a href="docs/util.html">util.py</a></code></td>

<td>Utilities, including <code>util.Counter</code>, which is particularly useful for q-learners.</td>

</tr>


<td><code><a href="docs/gridworld.html">gridworld.py</a></code></td>

<td>The Gridworld implementation</td>

</tr>


<tr>
<td><code><a href="docs/featureExtractors.html">featureExtractors.py</a></code></td>
<td>Classes for extracting features on (state,action) pairs. Used
	for the approximate q-learning agent (in qlearningAgents.py).</td>
</tr>


</table>
<h5><b>Files you can ignore</b></h5>

<table border="0" cellpadding="10">
<tr>

<tr>

<td><code><a href="docs/environment.html">environment.py</a></code></td>

<td>Abstract class for general reinforcement learning environments. Used 
by <code><a href="docs/gridworld.html">gridworld.py</a></code>.</td>

</tr>

<tr>

<td><code><a href="docs/graphicsGridworldDisplay.html">graphicsGridworldDisplay.py</a></code></td>

<td>Gridworld graphical display.</td>

</tr>

<tr>

<td><code><a href="docs/graphicsUtils.html">graphicsUtils.py</a></code>
</td>

<td>Graphics utilities.</td>

</tr>

<tr>

<td><code><a href="docs/textGridworldDisplay.html">textGridworldDisplay.py</a></code></td>

<td>Plug-in for the Gridworld text interface.</td>

</tr>

<tr>

<td><code><a href="docs/crawler.html">crawler.py</a></code></td>

<td>The crawler code and test harness. You will run this but not edit it.</td>

</tr>

<tr>

<td><code><a href="docs/graphicsCrawlerDisplay.html">graphicsCrawlerDisplay.py</a></code></td>

<td>GUI for the crawler robot.</td>

</tr>


</tbody> </table>

<p>&nbsp; </p>

<p><strong>What to submit:</strong> You will fill in portions of <code><a href="docs/valueIterationAgents.html">valueIterationAgents.py</a></code>, <code><a href="docs/qlearningAgents.html">qlearningAgents.py</a></code>, and <code><a href="docs/analysis.html">analysis.py</a></code> during the assignment. You should submit only these files.  Please don't change any others.</p>

<p><strong>Evaluation:</strong> Your code will be autograded for technical correctness. Please <em>do not</em> change the names of any provided functions or classes within the code, or you will wreak havoc on the autograder. However, the correctness of your implementation -- not the autograder's judgements -- will be the final judge of your score.  If necessary, we will review and grade assignments individually to ensure that you receive due credit for your work.

<p><strong>Academic Dishonesty:</strong> We will be checking your code against other submissions in the class for logical redundancy. If you copy someone else's code and submit it with minor changes, we will know. These cheat detectors are quite hard to fool, so please don't try. We trust you all to submit your own work only; <em>please</em> don't let us down. If you do, we will pursue the strongest consequences available to us.

<p><strong>Getting Help:</strong> You are not alone!  If you find yourself stuck on something, contact the course staff for help.  Office hours, section, and the newsgroup are there for your support; please use them.  If you can't make our office hours, let us know and we will schedule more.  We want these projects to be rewarding and instructional, not frustrating and demoralizing.  But, we don't know when or how to help unless you ask.

<p>&nbsp;</p>

<h3>MDPs</h3>

<p>To get started, run Gridworld in manual control mode, which uses the arrow keys:</p>

<pre>python gridworld.py -m</pre>

<p>You will see the two-exit layout from class.  The blue dot is the agent.  Note that when you press <em>up</em>, the agent only actually moves north 80% of the time.  Such is the life of a Gridworld agent!&nbsp; 
 
 <p>You can control many aspects of the simulation.&nbsp; 
 A full list of options is available by running:</p>

<pre> python gridworld.py -h</pre>

<p>The default agent moves randomly  </p>               

<pre> python gridworld.py -g MazeGrid</pre>

<p>You should see the random agent bounce around the grid until it happens upon an exit.&nbsp; 
   Not the finest hour for an AI agent.</p>

<p> <em>Note:</em> The Gridworld MDP is such that you first must enter a pre-terminal state (the double boxes shown in the GUI) and then take the special 'exit' action before the episode actually ends (in the true terminal state called <code>TERMINAL_STATE</code>, which is not shown in the GUI).&nbsp; If you run an episode manually, your total return may be less than you expected, due to the discount rate (<code>-d</code> to change; 0.9 by default).</p>

<p>Look at the console output that accompanies the graphical output (or use <code>-t</code> for all text).
    You will be told about each transition the agent experiences (to turn this off, use <code>-q</code>).&nbsp;</p>

<p>As in Pacman, positions are represented by <code>(x,y)</code> Cartesian coordinates 
   and any arrays are indexed by <code>[x][y]</code>, with <code>'north'</code> being 
	 the direction of increasing <code>y</code>, etc.&nbsp; By default, 
	 most transitions will receive a reward of zero, though you can change this 
	 with the living reward option (<code>-r</code>).&nbsp;</p>

<p><em><strong>Question 1 (6 points)&nbsp; </strong></em>Write a value iteration agent in <code>ValueIterationAgent</code>, which has been partially specified for you in <code><a href="docs/valueIterationAgents.html">valueIterationAgents.py</a></code>.&nbsp; Your value iteration agent is an offline planner, not a reinforcement agent, and so the relevant training option is the number of iterations of value iteration it should run (option <code>-i</code>) in its initial planning phase.&nbsp; <code>ValueIterationAgent</code> takes an MDP on construction and runs value iteration for the specified number of iterations before the constructor returns. 

<p>Value iteration computes k-step estimates of the optimal values, V<sub>k</sub>.  In addition to running value iteration, implement the following methods for <code>ValueIterationAgent</code> using V<sub>k</sub>.
<ul>
    <li> <code>getValue(state)</code> returns the value of a state.  
    <li> <code>getPolicy(state)</code> returns the best action according to computed values.
    <li> <code>getQValue(state, action)</code> returns the q-value of the (state, action) pair.&nbsp; 
</ul>

<p><em>Important:</em> Use the "batch" version of value iteration where each vector V<sub>k</sub> is computed from a fixed vector V<sub>k-1</sub> (like in lecture), not the "online" version where one single weight vector is updated in place.  The difference is discussed in <a href="http://www.cs.ualberta.ca/~sutton/book/ebook/node41.html">Sutton \& Barto</a> in the 6th paragraph of chapter 4.1.

<p><em>Note:</em> A policy synthesized from values of depth k (which reflect the next k rewards) will actually reflect the next k+1 rewards (i.e. you return &pi;<sub>k+1</sub>).  Similarly, the q-values will also reflect one more reward than the values (i.e. you return Q<sub>k+1</sub>).  You may assume that 100 iterations is enough for convergence in the questions below. 

<p>The following command loads your <code>ValueIterationAgent</code>, which will compute a policy and execute it 10 times. Press a key to cycle through values, q-values, and the simulation.  You should find that the value of the start state  (<code>V(start)</code>) and the empirical resulting average reward are quite close.

<pre>python gridworld.py -a value -i 100 -k 10</pre>

<p><em>Hint:</em> On the default BookGrid, running value iteration for 5 iterations should give you this output:

<pre>python gridworld.py -a value -i 5</pre>

<center>
<img src="value.png" width="50%" alt="value iteration with k=5"/>
</center>

<p>Your value iteration agent will be graded on a new grid.  We will check your values, q-values, and policies after fixed numbers of iterations and at convergence (e.g. after 100 iterations).  

<p><em>Hint:</em> Use the <code>util.Counter</code> class in <code><a href="docs/util.html">util.py</a></code>,
   which is a dictionary with a default value of zero.  The methods <code>totalCount</code> and <code>argMax</code> should simplify your code.</p>

<p><em><strong>Question 2 (1 point) </strong></em> Consider the policy learned on <code>BridgeGrid</code> with the default discount of 0.9 and the default noise of 0.2.
 <code>question2()</code> in <code><a href="docs/analysis.html">analysis.py</a></code> should return a pair <code>(discount, noise)</code> that changes only one of the default values for discount or noise so that your agent's optimal policy attempts to cross the bridge.  Noise refers to how often an agent ends up in a random successor state when they perform an action.&nbsp; Change either the noise or the discount, but not both.   The default corresponds to:
 
 <pre>python gridworld.py -a value -i 100 -g BridgeGrid</pre>
 
<p><em><strong>Question 3 (5 points) </strong></em> On the <code>DiscountGrid</code>, give any parameter 
values which produce the following optimal policy types or 
state that they are impossible by returning the string <code>'NOT POSSIBLE'</code>: 

<ol type="a">

<li>Prefer the close exit (+1), risking the cliff (-10)</li>

<li>Prefer the close exit (+1), but avoiding the cliff (-10)</li>

<li>Prefer the distant exit (+10), risking the cliff (-10)</li>

<li>Prefer the distant exit (+10), avoiding the cliff (-10)</li>

<li>Avoid both exits (also avoiding the cliff)</li>

</ol>

	<code>question3a()</code> through <code>question3e()</code> should each return a 3-item tuple of (discount, noise, living reward) in <code><a href="docs/analysis.html">analysis.py</a></code>. 

    <p><em>Note:</em> The arrows in each square indicate the agent's policy. For example, using a correct answer to 4(a), the arrow in (0,1) should point east, the arrow in (1,1) should also point east, and the arrow in (2,1) should point north.

<br>

<h3>Q-learning </h3>

<p>Note that your value iteration agent does not actually learn from experience.&nbsp; Rather, it ponders its MDP model to arrive at a complete policy before ever interacting with a real environment.&nbsp; When it does interact with the environment, it simply follows the precomputed policy (e.g. it becomes a reflex agent).  This distinction may be subtle in a simulated environment like a Gridword, but it's very important in the real world, where the real MDP is not available.&nbsp; </p>

<p><strong><em>Question 4 (5 points) </em></strong> You will now write a q-learning agent, which does very little on construction, but instead learns by trial and error from interactions with the environment through its <code>update(state, action, nextState, reward)</code> method.&nbsp; A stub of a q-learner is specified in <code>QLearningAgent</code> in <code><a href="docs/qlearningAgents.html">qlearningAgents.py</a></code>, and you can select it with the option <code>'-a q'</code>.  For this question, you must implement the <code>update</code>, <code>getValue</code>, <code>getQValue</code>, and <code>getPolicy</code> methods.

<p><em>Note:</em> For <code>getValue</code> and <code>getPolicy</code>, you should break ties randomly for better behavior. The <code>random.choice()</code> function will help.</p>

<p>With the q-learning update in place, you can watch your q-learner learn under manual control, using the keyboard:

<pre>python gridworld.py -a q -k 5 -m</pre>

Recall that <code>-k</code> will control the number of episodes your agent gets to learn.
Watch how the agent learns about the state it was just in, not the one it moves to, and "leaves learning in its wake."

<p><strong><em>Question 5 (2 points) </em></strong> Complete your q-learning agent by implementing epsilon-greedy action selection in <code>getAction</code>, meaning it chooses random actions epsilon of the time, and follows its current best q-values otherwise.

<pre>python gridworld.py -a q -k 100 </pre>

Your final q-values should resemble those of your value iteration agent, especially along well-traveled paths.  However, your average returns will be lower than the q-values predict because of the random actions and the initial learning phase.

<p> You can choose an element from a list uniformly at random by calling the <code>random.choice</code> function.  
You can simulate a binary variable with probability <code>p</code>
of success by using <code>util.flipCoin(p)</code>, which returns <code>True</code> with
probability <code>p</code> and <code>False</code> with probability <code>1-p</code>.

<p><strong><em>Question 6 (1 points) </em></strong> First, train a completely random q-learner with the default learning rate on the noiseless BridgeGrid for 50 episodes and observe whether it finds the optimal policy.

<pre>python gridworld.py -a q -k 50 -n 0 -g BridgeGrid -e 1</pre>

Now try the same experiment with an epsilon of 0. Is there an epsilon and a learning rate for which it is highly likely (greater than 99%) that the optimal policy will be learned after 50 iterations? <code>question7()</code> should return EITHER a 2-item tuple of <code>(epsilon, learning rate)</code> OR the string <code>'NOT POSSIBLE'</code> if there is none.  Epsilon is controlled by <code>-e</code>, learning rate by <code>-l</code>.

<p><strong><em>Question 7 (1 point) </em></strong> With no additional code, you should now be able to run a q-learning crawler robot:

<pre> python crawler.py</pre>

If this doesn't work, you've probably written some code too specific to the <code>GridWorld</code> problem and you should make it more general to all MDPs.  You will receive full credit if the command above works without exceptions.

<p>This will invoke the crawling robot from class using your q-learner.&nbsp; Play around with the various learning parameters to see how they affect the agent's policies and actions.&nbsp;&nbsp; Note that the step delay is a parameter of the simulation, whereas the learning rate and epsilon are parameters of your learning algorithm, and the discount factor is a property of the environment. &nbsp;
	
<h3>Approximate Q-learning and State Abstraction</h3>	

<p><strong><em>Question 8 (<b>1</b> points) </em></strong> Time to play some Pacman! Pacman will play games in two phases.
In the first phase, <em>training</em>, Pacman will begin to learn about the values of positions and actions.
Because it takes a very long time to learn accurate q-values even for tiny grids, Pacman's training games
run in quiet mode by default, with no GUI (or console) display.  Once Pacman's training is complete, 
he will enter <em>testing</em> mode.  When testing, Pacman's <code>self.epsilon</code>
and <code>self.alpha</code> will be set to 0.0, effectively stopping q-learning and disabling exploration, in order to allow Pacman to exploit his learned policy.  Test games are shown in the GUI by default.  Without any code changes you should be able to run q-learning Pacman for very tiny grids as follows:
	
<pre> python pacman.py -p PacmanQAgent -x 2000 -n 2010 -l smallGrid </pre>

Note that <code>PacmanQAgent</code> is already defined for you in terms of the <code>QLearningAgent</code> you've already written.   <code>PacmanQAgent</code> is only different in that it has default learning parameters that are more effective for the Pacman problem (<code>epsilon=0.05, alpha=0.2, gamma=0.8</code>). 

<p><em>Note:</em> If you want to experiment with learning parameters, you can use the option <code>-a</code>, for example <code>-a&nbsp;epsilon=0.1,alpha=0.3,gamma=0.7</code>.  These values will then be accessible as <code>self.epsilon, self.gamma</code> and <code>self.alpha</code> inside the agent. 
    
<p><em>Note:</em> While a total of 2010 games will be played, the first 2000 games will not be displayed because of the option <code>-x 2000</code>, which designates the first 2000 games for training (no output).  Thus, you will only see Pacman play the last 10 of these games.  The number of training games is also passed to your agent as the option <code>numTraining</code>.
    
<p><em>Note:</em> If you want to watch 10 training games to see what's going on, use the command:

<pre> python pacman.py -p PacmanQAgent -n 10 -l smallGrid -a numTraining=10</pre>

<br><br>
During training, you will see output every 100 games with statistics about how Pacman is faring. Epsilon is positive during training, so Pacman will play poorly even after having learned a good policy: this is because he occasionally makes a random exploratory move into a ghost. As a benchmark, it should take about 1,000 games  before Pacman's rewards for a 100 episode segment becomes positive, reflecting that he's started winning more than losing. By the end of training, it should remain positive and be fairly high (between 100 and 350).

<p>Make sure you understand what is happening here: the MDP state is the <em>exact</em> board configuration facing Pacman, with the now complex transitions describing an entire ply of change to that state.  The intermediate game configurations in which Pacman has moved but the ghosts have not replied are <em>not</em> MDP states, but are bundled in to the transitions.

<p>Once Pacman is done training, he should win very reliably in test games (at least 90% of the time), since now he is exploiting his learned policy.

<p>However, you'll find that training the same agent on the seemingly simple <a href="layouts/mediumGrid.lay"><code>mediumGrid</code></a> may not work well. In our implementation, Pacman's average training rewards remain negative throughout training.  At test time, he plays badly, probably losing all of his test games.  Training will also take a long time, despite its ineffectiveness.

<p>Pacman fails to win on larger layouts because each board configuration is a separate state with separate q-values.  He has no way to generalize that running into a ghost is bad for all positions.  Obviously, this approach will not scale.

<p><strong><em>Question 9 (<b>3</b> points) </em></strong> 
Implement an approximate q-learning agent that learns weights for features of states, where many states might share the same features.  Write your implementation in <code>ApproximateQAgent</code> class in <code><a href="docs/qlearningAgents.html">qlearningAgents.py</a></code>, which is a subclass of <code>PacmanQAgent</code>.
<!--Most of why Pacman fails for larger grids in the last problem is that there are many irrelevant details in each state, and so the same lessons must be learned many times.   However, just as with minimax, we can compute (approximate) values based on aspects of the state.   For example, if a ghost is about to eat Pacman, it's irrelevant which subset of the food in the grid is present, so we should be able to learn much about ghost fear from the ghost positions alone.   Alternatively, if a ghost is sufficiently far away it doesn't matter much exactly <em>how</em> far away or exactly where it is.  -->
	
<p><em>Note:</em>  Approximate q-learning assumes the existence of a feature function f(s,a) over state and action pairs, which yields a vector f<sub>1</sub>(s,a) .. f<sub>i</sub>(s,a) .. f<sub>n</sub>(s,a) of feature values. We provide feature functions for you in <code><a href="docs/featureExtractors.html">featureExtractors.py</a></code>. Feature vectors are <code>util.Counter</code> (like a dictionary) objects containing the non-zero pairs of features and values; all omitted features have value zero. 

<p>The approximate q-function takes the following form
<center>	
	<img  src="define-eqn1.png">	
</center>
<br>
where each weight w<sub>i</sub> is associated with a particular feature f<sub>i</sub>(s,a). In your code, you should implement the weight vector as a dictionary mapping features (which the feature extractors will return) to weight values. You will update your weight vectors similarly to how you updated q-values:
<center>	
	<br>
	<img  src="define-eqn2.png">	
</center>
<br>
Note that the <emph>correction</emph> term is the same as in normal Q-Learning.

<p>By default, <code>ApproximateQAgent</code> uses the <code>IdentityExtractor</code>, which assigns a single feature to every <code>(state,action)</code> pair. With this feature extractor, your approximate q-learning agent should work identically to <code>PacmanQAgent</code>.  You can test this with the following command:
	
<pre> python pacman.py -p ApproximateQAgent -x 2000 -n 2010 -l smallGrid </pre>

<p><em>Important:</em> <code>ApproximateQAgent</code> is a subclass of  <code>QLearningAgent</code>, and it therefore shares several methods like <code>getAction</code>.  Make sure that your methods in <code>QLearningAgent</code> call <code>getQValue</code> instead of accessing q-values directly, so that when you override <code>getQValue</code> in your approximate agent, the new approximate q-values are used to compute actions.

<p>Once you're confident that your approximate learner works correctly with the identity features, run your approximate q-learning agent with our custom feature extractor, which can learn to win with ease:

<pre> python pacman.py -p ApproximateQAgent -a extractor=SimpleExtractor -x 50 -n 60 -l mediumGrid </pre>

Even much larger layouts should be no problem for your <code>ApproximateQAgent</code>. (<em>warning</em>: this may take a few minutes to train)

<pre> python pacman.py -p ApproximateQAgent -a extractor=SimpleExtractor -x 50 -n 60 -l mediumClassic </pre>

<p><strong><em>Mini-Contest 2 (2 points extra credit) </em></strong> <code>SimpleExtractor</code> gives Pacman enough information to clear <code>mediumClassic</code>, but it doesn't tell Pacman anything about capsules, ghost hunting, dangerous corridors or dead-ends.  Design a feature extractor in <code>BetterExtractor</code> in <code><a href="docs/qlearningAgents.html">qlearningAgents.py</a></code> that presents more useful information to Pacman so that he can score as many points as possible on the <code>capsuleClassic</code> layout.  The contest will be judged by the following command.  The three teams with the highest average score in the last 10 games will receive some extra credit.  
    
<pre> python pacman.py -p ApproximateQAgent -a extractor=BetterExtractor -x 50 -n 60 -l capsuleClassic -g DirectionalGhost -q</pre>

<p><em>Hint:</em> Start with simple features and a small number of training games before trying anything complicated.  Learning can be finicky.

<p><em>Hint:</em> Learning will work much better if your features have a maximum absolute value of 1.  Shrinking the whole feature vector so that the sum of weights is less than 1 can help even further.  See <code>util.Counter.divideAll()</code> for scaling your feature vector.  

 <p><em>Congratulations! Now you have a smart Pacman.</em> 
    
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